Story of pendulum using STELLA

1. 1.0 Introduction.
1.0.1 Icon-based Model Building and Simulation Tool, STELLA
STELLA is a model that is easy to use and provided endless opportunities to explore. It also
have learning laboratory which give students, educators and researchers to study everything from
economics to physics, literature to calculus and also in biology. STELLA has an ability to
stimulate learning and inspiring the exciting moments of learning.
STELLA is used to simulate a system over time, jump the gap between theory and the real
world, enables students to creatively change systems, teach students to look for relationship,
clearly communicate system input and outputs, and demonstrate outcomes. Download trial is for
a month only. Students or educators that download for a trial should maximize the usage before
the expired date. This is because there a lot of advantage using STELLA.
1.0.2 Simple Pendulum.
A pendulum in simple harmonic motion oscillates about a central point. The pendulum is
a body suspended from a fixed point and assembled from a string with a weight at one end. It
swings freely to and fro under the action of gravity. From its rest position at a fixed period,
the pendulum will swing through small displacement. The period is the time for pendulum to
complete one or single oscillation. For example, pendulum move from one side and return to
that side, that is dependent on the length of the string and the acceleration of gravity. This is
𝐿
given by 𝑇=2 𝜋 . T is a period for one oscillation, L is a length of a string of the
𝑔
pendulum and g is the acceleration due to gravity. Notice that the weight of the bob does not
show up in this equation. This means that no matter what the weight, a bob that is suspended
on a certain length of string will take the same time to complete a cycles. The pendulum
passes twice through the arc during each period.
Galileo was the first to examine the pendulums’ unique characteristics. Galileo interested
in pendulums and he hit on the idea that pendulums have a constant period even when
moving at different angles. This comes from his observation on motions of chandelier
hanging in a cathedral and he noticed that it has a constant period even when moving at

2. different angles. Hence, Galileo began conducting with pendulums in order to examine if
their periods are indeed constant in 1602. He examined a variety of pendulums and claimed
that the period of each is totally independent of the size of the arc through which it passes
(displacement).
Today, we know that the period of the pendulum will remain constant as long as the
pendulum’s angle is not greater than about 20 degrees. If greater than 20 degrees, it is not
completely precise. Galileo also noticed that the period of the pendulum is not dependent on
weight of the material and pendulum’s period is influenced by its length alone. The longer
length of the string of the pendulum, the longer its period.
1.0.3 Pendulum Story Background and Context By Using A Learning Laboratory
Created With STELLA.
Figure 1 (a) : A learning laboratory created with STELLA on pendulum story

3. The simple pendulum is a small bob connected to the end of the string and is pulled a
short distance away from its rest position and released; it will begin to swing back and forth. The
type of motion faces by simple pendulum is simple harmonic motion.
It is assumed that the mass of the bob is concentrated at a point and that the mass of the
string is negligible. Time period, T (s) is the time taken for one oscillation. Frequency of the
oscillation is the number of oscillation simple pendulum made in one second: = 1/ T. The law of
a simple pendulum is:
 The period of a simple pendulum of constant length is independent of bob or ball
mass,
 The period of a simple pendulum is independent of the amplitude or displacement
of oscillation, provided it is small,
 The period of a simple pendulum is directly proportional to the square root of
length of the pendulum,
 The period of a simple pendulum is inversely proportional to the square root of
the acceleration due to gravity.
𝐿
𝑇=2 𝜋
𝑔
*where T (s) = time for 1 oscillation or cycle,
L (m) = length of pendulum ,
g = acceleration due to gravity (m/s2)
In this model, the relationship and the effect of different length of the string, bob mass
and initial starting position has on the motion of the pendulum are observed, ignoring the effect
of friction and air resistance. Then, when other forces are taken into account, the motion changes
are investigated.

4. 1.1 To Study The Relationship of Initial Starting Position of The Pendulum With The
Period (T).
In this experiment, there are four variables such as mass of ball (kg), initial displacement
(m), string length (m) and time taken to complete one oscillation. In the first part of the
experiment, the constant variables are string length and mass of ball. The manipulated variable is
the initial displacement. While, the responding variable is the time taken to complete one
oscillation or period, T (s). The graphs below shows the different initial displacement(m) vs time
(s).
Figure 2 (a): Initial displacement of -0.20m

5. Figure 2 (b): Initial displacement of 0.10m
Before started, the string length and mass of ball were set at 1.0 m and 1.00 kg. Then,
first initial displacement was set at -0.20 m and followed by -0.10m, 0.00m, 0.10m and 0.20m. In
this part, only use gravity. Each one peak or loop show one complete oscillation.
From the above graph in Figure 2 (a), at -0.20m initial displacement, the time taken for
pendulum to complete two oscillations is four seconds. To complete only one oscillation, the
pendulum needs two seconds. Like in Figure 2 (a), graph in Figure 2 (b) also show four seconds
to complete two oscillations and needs two seconds to complete one oscillation but its initial
displacement is -0.10m.

6. Figure 2 (c): Initial displacement of 0.00m
Figure 2 (d): Initial displacement of 0.10m

7. Figure 2 (e): Initial displacement of 0.20m
However, when initial displacement is 0.00m as in Figure 2 (c), the graph is constant and
have no peak. From the graph, we know that as the time passes, the displacement is still zero
because the pendulum is not swinging and have no displacement. No displacement means that no
distance and no direction by pendulum. In Figure 2 (d) and Figure 2 (e), the time taken for the
pendulum to complete two oscillations are four seconds and take only two seconds to complete
one oscillation although the displacements are differ.
The Figure 2 (a), Figure 2 (b), Figure 2 (d) and Figure 2 (e) have constant period of the
pendulum because they have only little bit different in displacement. The Figure 2 (c) only show
constant graph because of pendulum does not oscillate. From this result obtained, we know that
the period of the pendulum or the time taken to complete oscillation for a pendulum will remain
constant as long as the pendulum angle displacement is not greater than 20 degrees.

8. 1.2 To Study the Relationship of Mass of Ball’s Pendulum with Number of Oscillation
Within 2 Seconds.
By using Stella software, we also can study the relationship of ball’s mass with the
number of oscillation within 2 seconds. We can set up experiment by set similar or fixed
variable that is string length and initial displacement. So, the manipulated variable is mass of ball
and responding variable is number of oscillation within 2 seconds.
Every student has their own hypothesis. My hypothesis is mass of ball’s pendulum effect
the number of oscillation within 2 seconds. For me, as the mass of ball’s pendulum increases, the
number of oscillation within 2 seconds also increases. The graphs below show the number of
oscillations by different mass of ball. To determine the number of oscillations, we just look at
the peak at graph. The one peak represents one oscillation; two peaks represent two oscillations
and so on.
Figure 3 (a) : 0.01kg ball

9. From the figure 3 (a), the number of oscillations in 2 seconds is three oscillations with the
constant or fixed displacement of 0.10 m. this is because there are three peak at the 2 seconds.
The mass of ball used is 0.01kg and it is smallest mass used. In this experiment, we used gravity
only and not include friction and driving force. So, we need to use another mass of ball and
repeat the experiment with different mass of ball. The experiment is repeated by using 0.50kg,
1.00kg, 1.50kg and 2.00kg.
Figure 3 (b) : 0.50kg ball Figure 3 (c) :1.00kg ball
Figure 3 (d) : 1.50kg ball Figure 3 (e) : 2.00kg ball

10. By using 0.50kg of ball, the graph is still same with the previous graph. We can see that
in 2 seconds, the number of oscillations are also three although the mass of ball used is different
in 0.49kg. the graphs of 1.00kg, 1.50kg and 2.00kg ball also show same graph that have 3 peaks
in 2 seconds. From all graphs, we know that the mass of ball whether high or less, it does not
effect the number of oscillations in two seconds. Hence, my hypothesis about the mass of ball’s
pendulum effect the number of oscillation in 2 seconds are not accepted.
This STELLA software is interesting to use and make learning session fun. It attract
students to explore the pendulum story by make experiment using STELLA software. Back to
above topic to explain the graph. The driving force for a pendulum used above is only gravity. If
the pendulum has twice the mass, gravity pulls twice as hard. Mass is also show how hard an
object resists the force it feels. For example, it more difficult to start motion for a bowling ball
than for a ping-pong ball.
A pendulum that have a twice the mass feels twice the pull, but also has the twice the
resistance to that pull. These two effects balance out and the twice mass still experiences the
same effect. The mass of ball’s pendulum does not affect how it moves. This is because the force
accelerating the pendulum comes from its weight.
The more massive the pendulum is, results in greater its weight, in strict proportion. The
inertia, that is, the resistance of the pendulum to acceleration by a force, is also in strict
proportion to its mass. Since both the force and inertia vary in strict proportion to the mass, the
two effects cancel out and the acceleration is independent of mass. Hence, the more massive ball,
the more force is required to make it accelerate at a given rate. The more massive ball, the more
force gravity exerts on it. The net result is that acceleration from the force of gravity does not
change as an object's mass changes.

11. 1.3 To Study The Relationship Between String Length With Period , T (s).
After studied the relationship of initial displacement with period and mass of ball with
number of oscillation within time given, now relationship between string lengths with period also
can be study by using STELLA. In this experiment, the motion of a swinging bob of a pendulum
will be measures using STELLA to prove or disprove the stated hypothesis. Equations relating
the motion of each mass must be used to determine and compare their periods.
𝐿
𝑇=2 𝜋
𝑔
Figure 4 (a) : 0.1 m string length

12. Figure 4 (b) : 0.5 m string length
From the above, these two graphs show different number of oscillations within 4 seconds. In
Figure 4 (a), the number of oscillations within 4 seconds is more or less than 6 oscillations but in
figure 4(b), the number of oscillations within 4 seconds is more or less than 3 oscillations. So, to
calculate the periods, we can use the equations,
𝐿
𝑇=2 𝜋
𝑔
The period, T for the 0.1m string length is
0.1𝑚
𝑇=2 𝜋 𝑚
9.8 2
𝑠

13. 𝑇 = 0.63𝑠
This mean that the pendulum with string length of 0.1m have one complete oscillation at 0.63
seconds. The period for 0.5m string length is also calculated by using that equation. Then, the
number of oscillations for 4 seconds is,
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝑇=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛
4𝑠
0.63𝑠 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛
4𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛 =
0.63𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛 = 6.35 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛
Figure 4 (c) : 1.0m string length

14. Figure 4 (d) : 1.5m string length
Figure 4 (e) : 2.0m string length

15. In Figure 4 (c), the pendulum have one complete oscillation in 2 seconds and two
complete oscillation in 4 seconds. Then, we can used below equation to calculate the period.
1.00𝑚
𝑇=2 𝜋 𝑚
9.8 2
𝑠
𝑇 = 2.00𝑠
This proved that STELLA shows an accuracy also in graph because T value get from the graph
are same with the calculation.
In Figure 4 (d) and 4 (e), the number of oscillation within 4 seconds are more than 1
oscillation and less than 2 oscillation. So, to get the period of oscillation, we must use the
equation that have been used before.
The figure below shows the graph displacement versus time of combined string length.
There are also table that include string length, period, mass of ball, initial displacement. The
table below are used to compare the period of different string length used.
Mass of ball (kg) Initial displacement String length (m) Period, T (s)
(m)
1.0 0.1 0.1 0.63
1.0 0.1 0.5 1.42
1.0 0.1 1.0 2.00
1.0 0.1 1.5 2.46
1.0 0.1 2.0 2.84
Table 1 : Period on different string length.

16. Figure 4 (f) : Combined string length
The pendulum will take more or less time to oscillate, depending on its length and
acceleration due to gravity. From the experiment using STELLA, the longer the string length, the
longer period taken to complete one oscillation. The shorter the string length, the shorter period
taken to complete one oscillation.

17. 1.4 Conclusion
Again, there is no relationship between mass and period, while for small amplitude or
displacement, there is only the weakest relationship between the displacement and the period.
Hence, the period, T must be proportional to square root of string length, L and inversely
proportional to square root of acceleration of gravity, g was found by Galileo.
This STELLA software makes learning easier and interactive. By visual, we can look the
difference of the graphs when we used the different string length. The difference of the graphs
are difference number of peaks resulted due to different string length. We are easily analyzed the
graph show and can test our hypothesis, and lastly make conclusion.
Using of computer simulation programs in education helps students more familiar with
use of the computer in education. It offers the opportunity to students to experiment with
phenomena which cannot normally be experimented with in the traditional way. Bork (1981)
remarks: ‘Simulations provide students with experience that may be difficult or impossible to
obtain in every day life’. For example, it is not possible to experiment with an economic system.
Only nature and content of the system that teacher can discuss in the class and of course
experimenting be useful because can generate insight into the functioning of the economic
system.
Foster (1984) says that, simulation can be entertaining because of dramatic and game-like
components. Some students have no feeling to learn something that abstract. This make they do
not have interest in learning. By use computer simulation in school in Malaysia, students are
more feeling for reality in some abstract fields of learning.
The other advantage is teacher or trainee can just use computer simulation program to
carry out experiment and exercise as much as necessary. This is because the apparatus that
needed in the experiment is too expensive. Simulation also often goes hand in hand with
visualization. The students can adjust the manipulated variable according to what they want to
observe. The results of changes are directly shown on the screen. This generally appeals to the
students. Not only that, the flexibility of the computer simulation programs motivates student
whether intrinsic or extrinsic.
There are also disadvantages of using computer simulation programs in education.
Computer simulation programs look well from a technical point of view, but they are difficult to
fit into a curriculum. It also cannot be adapted into different student level within a class. Other
than that, as it need computer to run the simulation programs, it also need electric source to turn
on computer. This means that only main source is electric current and without electric source, the
computer simulation programs cannot be run.

18. Reference (s)
Anonymous (2012). The Pendulum. Retrieved on November 17, 2012 from
http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/pendulum_exp.pdf
Anonymous (2012). Pendulum Motion. Retrieved on November 17, 2012 from
http://www.physicsclassroom.com/class/waves/u10l0c.cfm
Claver Pedzisai Bhunu (2010). A Mathematical Analysis of Alcoholism. Retrieved on November
17, 2012 from http://www.wjms.org.uk/wjmsvol08no02paper05.pdf
Garrett, B. (2012). Simple Harmonic Motion – Part II. Retrieved on November 17, 2012 from
http://www.educationalelectronicsusa.com/p/shm-II.htm
Rik Min (2012). Advantages and Disadvantages of Model-Driven Computer Simulation.
Retrieved on November 17, 2012 from
http://projects.edte.utwente.nl/pi/papers/simAdv.html